The use of approximate motion models for solving boundary value problems in astrodynamics

Аuthors

Panchukov A. A.

Abstract

The feature that characterizes boundary value problems in astrodynamics is the absence of an analytical relation between arguments and terminal functions. Such relation can only be obtained through numerical integration of a system of differential motion equations, which makes it difficult to determine an initial approximation guaranteeing convergence of the iterative process of the search for solution to a system of non-linear equations, and the process becomes very time-consuming. That is the reason for widespread use of this method, which is based on approximate motion models being used for searching an initial approximation of the arguments vector and its subsequent updating. The use of method proposed in this paper does not require a numerical calculation of partial derivatives matrix of terminal conditions vector with respect to arguments of boundary value problem, while the search for and correction of the initial approximation can be performed using the same algorithm.
Algorithms for approximate motion models are systematically used for solving the flight profile synthesis problems in this method. The universally used method for solving boundary value problems in maneuvering in their precise statement is the method of searching for a vector of arguments and correcting it in order to minimize boundary condition errors on the basis of relations for approximate model of motion.
It is justified to use the spectral radius value of the iteration process matrix in order to evaluate conditions for the method convergence. The paper analyses the factors affecting to the method convergence. Numerical estimates have been obtained for the applicability of the model of motion along orbits that are close to circular orbits for correction of misses when solving maneuvering problems for low-flying SC.
To solve the problems of maneuvering in open intermediate orbits the ballistic coefficient was used as parameters of the precise computational model and the value reciprocal to the thrust vector modulus, because the approximate model has pulsed approximation of the trajectory powered portions in addition to the fact that the atmospheric drag was not taken into account. The described technique had turned out to be effective up to conditions where solution didnt exist because of physical constraints.

Keywords:

models of motion, , convergence conditions of iteration, maneuvers in low orbits

References

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